It would be infuriating if Burnett signed elsewhere. He had previously said that if he didn't retire, he'd pitch for the Pirates. Fine, and if he chose to retire, no one would blame him. The Pirates didn't extend a qualifying offer. Then Burnett said he'd take a week to think about it, and a week stretched into three months. Meanwhile, the Pirates have done very little this offseason, while maintaining that they have the "flexibility" to re-sign Burnett. And now that the entire first base market is kaput and there isn't much left on the pitching market either, Burnett wants to pitch, and he might sign with another team. Burnett lives near Baltimore, and the Orioles need rotation help, so that would be one obvious fit.
Of course, we don't know the whole story. Just yesterday, Jeff Banister tweeted a cryptic goodbye message to Burnett. The Pirates have said that they didn't want to pay top dollar for Burnett, and their refusal to extend a qualifying offer to Burnett was likely part of that. John Perrotto reported the other day that the Pirates only offered Burnett $8.5 million, which certainly is far less than he's worth. Then again, Burnett is likely financially secure and may not really need to make a lot of money, and if he truly only wanted to pitch for the Pirates, it wouldn't make sense for them to bid against themselves. There's a lot of noise here, and it's very hard to tell where the signal is. But I would be pretty annoyed with both Burnett and the Pirates if he ended up signing somewhere else.